How many committee of five persons with a chairperson can be selected from 12 persons.

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together.

Find the number of positive integers greater than 6000 and less than 7000 which are divisible by 5, provided that no digit is to be repeated.

There are 10 persons named P1
, P2 , P3 , ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1
 must occur whereas P4 and P5
 do not occur. Find the number of such possible arrangements.

There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.

A box contains two white, three black and four red balls. In how many ways
can three balls be drawn from the box, if atleast one black ball is to be included in the draw.

Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated.

If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?